I think Betelgeuse is something like an anomaly. He´s not part of Satella´s/Emilia´s plan.
As for the neet-thing: This anime has made it a point to show how pathetic otaku/neets are. The past couple of episode haven´t just been Subaru being pathetic, they really put it on the nose that his patheticness stemmed from him being an otaku. If we assume that that is a central theme of this show, then I can also see it being important to the election process of Satella´s. Something along the lines of:
"After decades of studying, I´ve found that there is one kind of human that is easier influencable than anybody else. That kind is called 'otaku' or 'hikkikomori', and they are prone to becoming a girl´s servant, as long as she is cute of appearance. Instead of convincing capable fighters to aide me in my mission to lead this country, it proved to be much less of a hassle to simply pick one of these desperate husks of a human being. It hasn´t quite worked out yet, but I´m using the past experience and act differently accordingly. With you, Subaru, I think I´ve finally found the perfect candidate."
" ... what ... are you saying ... EMILIA?!"
"Now die and keep trying your best to put me on the throne."
Anime ends.